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66 lines
1.8 KiB
Plaintext
66 lines
1.8 KiB
Plaintext
/*
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* sumsq - find unique two positive integers whose squares sum to a given prime
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*
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* Copyright (C) 1999 David I. Bell
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*
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* Calc is open software; you can redistribute it and/or modify it under
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* the terms of the version 2.1 of the GNU Lesser General Public License
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* as published by the Free Software Foundation.
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*
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* Calc is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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* Public License for more details.
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*
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* A copy of version 2.1 of the GNU Lesser General Public License is
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* distributed with calc under the filename COPYING-LGPL. You should have
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* received a copy with calc; if not, write to Free Software Foundation, Inc.
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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* @(#) $Revision: 30.1 $
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* @(#) $Id: sumsq.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
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* @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/sumsq.cal,v $
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*
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* Under source code control: 1990/02/15 01:50:37
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* File existed as early as: before 1990
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*
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* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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*/
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/*
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* Determine the unique two positive integers whose squares sum to the
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* specified prime. This is always possible for all primes of the form
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* 4N+1, and always impossible for primes of the form 4N-1.
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*/
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define ss(p)
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{
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local a, b, i, p4;
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if (p == 2) {
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print "1^2 + 1^2 = 2";
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return;
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}
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if ((p % 4) != 1) {
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print p, "is not of the form 4N+1";
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return;
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}
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if (!ptest(p, min(p-2, 10))) {
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print p, "is not a prime";
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return;
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}
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p4 = (p - 1) / 4;
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i = 2;
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do {
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a = pmod(i++, p4, p);
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} while ((a^2 % p) == 1);
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b = p;
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while (b^2 > p) {
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i = b % a;
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b = a;
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a = i;
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}
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print a : "^2 +" , b : "^2 =" , a^2 + b^2;
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}
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